Note that using the traditional Softmax output layer would not allow for a closed-form solution in order to propagate and marginalize the uncertainty associated with the output \({Y}\) . Instead, we propose to employ a hierarchical binary decomposition similar to what was employed by [1]} ([1]}). For that, each class is encoded in a binary tree with \(\mathtt {H}=\lceil \log _2(\mathtt {K})\rceil \)  layers, and which is defined by \(\mathtt {Y}=\mathtt {K}-1\)  hidden states when \(\log _2(\mathtt {K})\in \mathbb {Z}^+\) .
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